# Slice Sampling of the Dirichlet Process Mixture Model with a prior on alpha ```r DPMGibbsN_parallel( Ncpus, type_connec, z, hyperG0, a = 1e-04, b = 1e-04, N, doPlot = TRUE, nbclust_init = 30, plotevery = N/10, diagVar = TRUE, use_variance_hyperprior = TRUE, verbose = TRUE, monitorfile = "", ... ) ``` ## Arguments - `Ncpus`: the number of processors available - `type_connec`: The type of connection between the processors. Supported cluster types are `"SOCK"`, `"FORK"`, `"MPI"`, and `"NWS"`. See also `makeCluster`. - `z`: data matrix `d x n` with `d` dimensions in rows and `n` observations in columns. - `hyperG0`: prior mixing distribution. - `a`: shape hyperparameter of the Gamma prior on the concentration parameter of the Dirichlet Process. Default is `0.0001`. - `b`: scale hyperparameter of the Gamma prior on the concentration parameter of the Dirichlet Process. Default is `0.0001`. If `0`, then the concentration is fixed set to `a`. - `N`: number of MCMC iterations. - `doPlot`: logical flag indicating whether to plot MCMC iteration or not. Default to `TRUE`. - `nbclust_init`: number of clusters at initialization. Default to 30 (or less if there are less than 30 observations). - `plotevery`: an integer indicating the interval between plotted iterations when `doPlot` is `TRUE`. - `diagVar`: logical flag indicating whether the variance of each cluster is estimated as a diagonal matrix, or as a full matrix. Default is `TRUE` (diagonal variance). - `use_variance_hyperprior`: logical flag indicating whether a hyperprior is added for the variance parameter. Default is `TRUE` which decrease the impact of the variance prior on the posterior. `FALSE` is useful for using an informative prior. - `verbose`: logical flag indicating whether partition info is written in the console at each MCMC iteration. - `monitorfile`: a writable connections or a character string naming a file to write into, to monitor the progress of the analysis. Default is `""` which is no monitoring. See Details. - `...`: additional arguments to be passed to `plot_DPM`. Only used if `doPlot` is `TRUE`. ## Returns a object of class `DPMclust` with the following attributes: - **`mcmc_partitions`:**: a list of length `N`. Each element `mcmc_partitions[n]` is a vector of length `n` giving the partition of the `n` observations. - **`alpha`:**: a vector of length `N`. `cost[j]` is the cost associated to partition `c[[j]]` - **`listU_mu`:**: a list of length `N` containing the matrices of mean vectors for all the mixture components at each MCMC iteration - **`listU_Sigma`:**: a list of length `N` containing the arrays of covariances matrices for all the mixture components at each MCMC iteration - **`U_SS_list`:**: a list of length `N` containing the lists of sufficient statistics for all the mixture components at each MCMC iteration - **`weights_list`:**: a list of length `N` containing the logposterior values at each MCMC iterations - **`logposterior_list`:**: a list of length `N` containing the logposterior values at each MCMC iterations - **`data`:**: the data matrix `d x n` with `d` dimensions in rows and `n` observations in columns - **`nb_mcmcit`:**: the number of MCMC iterations - **`clust_distrib`:**: the parametric distribution of the mixture component - `"gaussian"` - **`hyperG0`:**: the prior on the cluster location ## Examples ```r # Scaling up: ---- rm(list=ls()) #Number of data n <- 2000 set.seed(1234) # Sample data d <- 3 nclust <- 5 m <- matrix(nrow=d, ncol=nclust, runif(d*nclust)*8) # p: cluster probabilities p <- runif(nclust) p <- p/sum(p) # Covariance matrix of the clusters sdev <- array(dim=c(d, d, nclust)) for (j in 1:nclust){ sdev[, ,j] <- matrix(NA, nrow=d, ncol=d) diag(sdev[, ,j]) <- abs(rnorm(n=d, mean=0.3, sd=0.1)) sdev[, ,j][lower.tri(sdev[, ,j], diag = FALSE)] <- rnorm(n=d*(d-1)/2, mean=0, sd=0.05) sdev[, ,j][upper.tri(sdev[, ,j], diag = FALSE)] <- (sdev[, ,j][ lower.tri(sdev[, ,j], diag = FALSE)]) } c <- rep(0,n) z <- matrix(0, nrow=d, ncol=n) for(k in 1:n){ c[k] = which(rmultinom(n=1, size=1, prob=p)!=0) z[,k] <- m[, c[k]] + sdev[, , c[k]]%*%matrix(rnorm(d, mean = 0, sd = 1), nrow=d, ncol=1) #cat(k, "/", n, " observations simulated\n", sep="") } # hyperprior on the Scale parameter of DPM a <- 0.001 b <- 0.001 # Number of iterations N <- 25 # do some plots doPlot <- TRUE # Set parameters of G0 hyperG0 <- list() hyperG0[["mu"]] <- rep(0, d) hyperG0[["kappa"]] <- 0.01 hyperG0[["nu"]] <- d + 2 hyperG0[["lambda"]] <- diag(d)/10 nbclust_init <- 30 if(interactive()){ library(doParallel) MCMCsample <- DPMGibbsN_parallel(Ncpus=2, type_connec="FORK", z, hyperG0, a, b, N=1000, doPlot=FALSE, nbclust_init=30, plotevery=100, gg.add=list(ggplot2::theme_bw(), ggplot2::guides(shape = ggplot2::guide_legend(override.aes = list(fill="grey45")))), diagVar=FALSE) } ``` ## See Also `DPMGibbsN` ## Author(s) Boris Hejblum

DPMGibbsN_parallel function